Week 12: Report and Reflection

Well, I went into this course feeling very incapable of teaching mathematics since I have a poor background in that subject area. Now I feel very opposite to what I wrote in my first blog post. I feel very confident in my ability to teach math and I think that this class allowed for exploration of some really great tools and resources.

I found the Great Games Exploration to be especially helpful. I used Dirt Bike Proportions the other day at my placement and the students gave feedback saying that it was their favourite activity. I believe that digital games are so important to 21 century teaching, since games are relatable to students. They also enjoy the challenge without having any academic penalty as to incorrect answers, since in games they can always play again.

The digital portfolio for teaching was also a great resource that we were able to curate ourselves. I think it is beneficial that we were each others guinea pigs for potential lessons and activities we would implement in our classrooms. This allowed us to encounter what would be unforeseen mishaps with the activities and be aware of how we could adapt the activities to improve.

Through these activities I thought that the most beneficial ones were those that allowed students to collaborate with others or work in groups, that allowed for some type of experience, that had some tactile or visual component, and asked students to use what is familiar to them and relate it into a new context.

My goal for teaching math this block and beyond is to implement activities and lesson with these outcomes and allow students to explore mathematics through meaningful experiences.


Good luck at your teaching blocks everyone!

Week 11: Report and Reflection

This week we finalized our learning activity presentations with computational strategies. Basically, how we could implement technology into the classroom while teaching math. Amberley showed a Youtube video on fractions. This was effective because videos can help to engage students by taking what would be a confusing topic, breaking it down, and adding humour and visuals to capture attention and help students to better understand the topic. Amberley brought up a great point, that too many videos may be too routine for students, and then they start to get boring and predictable. Videos are good to use once in a while to perk the class back up again when they start to lose interest. Jake also made a great point, that the resources are already there for us and we don't have to constantly be reinventing the wheel. These sources are here for a reason, and that is to help us help students.

Madison had us playing Ratio Stadium in pairs. I think that these types of games allow for practice of mental math but also evoke friendly competition in the classroom. This is a great way to keep students engaged and also work together to solve problems. Maybe students at different grade levels could be partnered together so that the lower grade level student can learn from the higher level student, and also not feel as though they are losing at the game because they have help with them.

You can play Ratio Stadium here 

I really liked how Victoria looked at ways in which technology can be used as a way to consolidate a unit and check for students readiness in preparation for tests. Using Kahoot allows teachers to see how each individual student is answering and can better evaluate their position in the unit that way. The teacher can also see what questions the class is mostly getting wrong, so they know whether to work on it more before a test or not. Kahoot kept everyone in the class so engaged and it allows for something new and interesting to happen in the class. We are trying to make math as fun and engaging as possible for students and break the stigma of boring old mathematics! I think if our schools have access to technology we should harness the opportunity to bring it in as much as possible. 

Week 10: Report and Reflection

This week our class focused on Data Management & Probability. Data Management & Probability is a large topic to cover because there are ways in which we collect and describe data, ways that we display and analyze our data, and also how do we measure the likelihood of the next event based on our data.

I thought that Jeff's activity was an appropriate way to get students engaged with the ways in which we collect and organize data through the mean, median and mode. After going through some modelling he asked use within our groups to find the mean, median, mode and range with our collection of shoe sizes. He also presented the question in the context of a real-life situation. We were to imagine we were a shoe company and by calculating the the mean, median and mode of our data we were able to see why a company would want to know this information, because it helps to better plan with manufacturing. Activities like this allow for students to connect reasons where we use mathematics in real-life and also why we use mathematics.

Asma's activity clearly identified the uses of bar graphs and how to represent data. What I find to be most effective in teaching how to represent data is the use of asking students questions that pertain to their interests. Asking them about favourite colours, or shoe sizes allows them to record what they are familiar with in order to simplify the concept. I also enjoyed the activity itself which allowed students to work with a partner to record the rolls of their dice. This presented a way of collecting random data and also made the activity feel like playing a game.

Asma's Activity
Chamberlain, 2015 (C)

People Graph
Small, Marian. Making Math Meaningful. p.520

Representational Graph
Small, Marian. Making Math Meaningful. p.521

Making Math Meaningful also identified various ways of representing and communicating data. I think having students create concrete graphs, people graphs or with representational objects, are an effective way for having students visualize the concept of graphing more thoroughly. People graphs suit the contexts where students are graphing personal data, such as choices or opinions. (p. 520) Representational graphs use objects or manipulatives. Asking students to create people graphs will help students communicate graphic visually and also orally because the whole group could create a discussion based on how they have graphed themselves. Representational graphs using objects would allow for visual comparisons and also connecting with real life objects. I feel that using concrete methods of graphing would be a necessary step to take prior to having students record actual graphs on chart paper because they would have a better sense of the purpose of graphing.







Resources:
Small, Marian. Making Math Meaningful to Canadian Students, K-8. 2nd Edition. Nelson: Toronto, 2013.

Week 9: Report and Reflection

What I am enjoying most about the readings from the text book is that it allows us to distinctly define the topics of study. For instance the book explains measurement and that "it is about assigning a numerical value to an attribute of an object, relative to another object called a unit. Usually, you measure to have a sense of the size of an object compared to other objects whose size you know. A greater measurement implies that one object has 'more' of a particular attribute than another." (p. 412) I find that it is helpful, as a teacher candidate unfamiliar with mathematics, that it is extremely useful to be able to define topics in this way. It helps for a better understanding when revisiting the methods and work involved in that topic.

I also learned about addressing Measurement Principles in the classroom (p.413):

• Different measurement attributes of the same object are not always related, so it is possible for an object to be large in one way and to be small in another
• Sometimes you measure directly and sometimes you measure indirectly
• Most measurements can be determined in more than one way
• Familiarity with certain measurement referents helps you estimate
• There is more than  one possible unit that could be used to measure an item, but the unit chosen should make sense for the object.
• In order to measure, a series of uniform units must be used, or a single unit must be used repeatedly

Lory Evans 2nd Grade Page. URL: http://bit.ly/1NyG7FL

In going over these principles, I can see the importance of all of these would be in teaching measurement and would have to be carefully considered while constructing a unit on measurement.
Reflecting on the class presentations, I was able to see how our presenters were able to construct various measurement principles within their chosen activity.

I can envision using Tim's activity of asking students to come up and measure their height. Not only is this engaging and as a fourth grade student probably very exciting to come up and be measured in front of the class. But this activity also inadvertently instills various measurement principles within it.  This activity presented the principle that "sometimes you measure directly and sometimes you measure indirectly". We were asked to estimate the heights of our teacher candidates after having our heights marked on the board, this would be indirect measurement because we are guessing based on what we know about measurement in real life. There is also the principle tied into this that "most measurements can be determined in more than one way," and also "familiarity with certain measurement referents helps you estimate." For example, Dylan pictured the height of a meter stick and envisioned it's length to compare what the heights may be. For myself, I knew my height in feet and inches (imperial system) and I used my height to compare to what the other heights may be. Once I started with the imperial system I had to change this to metric, and I did not know how to do this using Tim's chart, but what I did know is that there are 12 inches in every foot, and about 2.5 cm in every inch. I am 5 ' 2", so I converted my feet into inches, 5 feet x 12 inches = 60 + 2 extra inches = 62 inches. And if one inch equals 2.5 cm, than 62 inches x 2.5 cm = 155 cm. Using this strategy I was able to estimate the heights effectively which were only very few centimetres off from the actual heights. It is interesting the different methods students will use to make their estimates.

Anthony's activity presented area and perimeter and what I would like to make note of from this are the various ways students were able to calculate area of misshaped figures. Different students came up with ways they would split the figure, and some students would calculate the whole area and use subtraction to take away the areas that did not exist in the shape. Again, it is interesting to encounter to various ways students will approach problem solving and what they can envision in their heads.

Chamberlain, 2015 (C)

What interests me about the chapter that did not really come up in the activities is qualitative measurement - although Tim did describe the distinction between qualitative and quantitative measurement - I am curious about this topic because it presents how we can measure without using rulers. We can measure with other tools, almost anything we can find, in order to get an approximate measurement. Below is an image from page 436 of the text book, which uses pennies to calculate area. For students just learning area this would be a great way to explain the concept of area, being that it is the measurement that fills the entire inside of a shape. This is also effective because it builds a schema of measurement for students, if they are in a real world situation where they may need to estimate, they can figure out that a penny is almost 2cm wide, and would be able to envision pennies or physically line pennies up to come up with a measurement.

Small, Marian. Making Math Meaningful. p.436

Resources:
Small, Marian. Making Math Meaningful to Canadian Students, K-8. 2nd Edition. Nelson: Toronto, 2013.

Week 7: Report and Reflection

This week our class focused on patterning and algebra. The main idea with patterns is that they represent identified regularities, in other words, we are able to look at representations in a way that we recognize that there is a regular consistency between them in order to come up with the next variant.

Some core ideas about patterns, from the textbook are:

• Patterns can be represented in variety of ways 
• Some ways of displaying data highlight patterns
• Much of other strands in mathematics is built on pattern foundation
• Algebra is a way to represent and explain mathematical relationships and to describe and analyze change
• Relationships between quantities can be described efficiently using variables

To have our students determine patterns we would look at a visual example or a stream of numbers and decipher what the pattern here is:

https://www.mydigitalchalkboard.org/portal/default/Content/Viewer/Content?action=2&scId=306591&sciId=18291

With this image, we can see the pattern is that a square is being added to each corner of the X and keeps expanded within the next steps.

But with algebra, we would decipher the formula which is a underlying way to describe what is happening in these images. So algebra explains the mathematical relationship to describe patterns. 

So the formula for the above image 4(Input) +1 = (Output). 4 is decided to be the constant because 4 squares are always added to each image. The input would vary depending on which step we are on and then we add 1 to get the output. 

So for example 

Step 1:  4(1)+1=5

Step 2: 4(2)+1=9

Step 3: 4(3)+1=13

Step 4: 4(4)+1=17

_________________________________________________________________________________

For our activity presentations I found our presenters to be extremely well researched, this is probably one of the most complicated topics to teach, as we seen with a lot of confusion today, so it was great that our presenters were knowledgable with the topic and prepared. 

I thought that Brittany did an exceptional job modelling. The way she segued from introduction to activity was very clear and she got our minds on with questions as well as involving us in her example in which she clearly modelled how the activity was meant to be done and how it would be shown and written before she let us do it ourselves. I think this is so important because it is not always enough to teach a lesson and give an activity and have students go in without explicitly presenting what needs to be done. 

Brett should be given a lot of credit for choosing an activity which relates to maybe one of the most complicated subjects that we have come across in the class, algebra. He was knowledgable about his topic, which a good teacher needs to be when tackling a subject that confuses about 95% of the class. What I enjoyed most about his presentation was how much we genuinely learned from it as a class to come up with answers and better understand algebraic equations. For this activity we worked in groups to to determine the relationships between the input/output numbers to come up with the relationships and equations. What was strong about the activity he chose was that it fits into a social constructivist method of teaching, which emphasizes the collaborative nature of learning. I also liked the terminology he introduced with "input" and "output," and how it was laid out in the chart. I have never heard or seen algebra presented like this before and I think it makes everything much more clear and organized.

Brittany's Activity: Use the 3 questions to come up with the colours and amounts you will use to make up your pattern,
in each box create the next step to expand your pattern
[Chamberlain, 2015 (C)]

So the last part of the class we worked within groups to determine the pattern on our worksheet with the expanding X's (similar to the X pattern I posted above). In Figure 1 you will see my group misunderstood the instruction to represent the pattern change and we thought we had to come up with a way to represent it in a different way so we thought to do a real life situation with cars in a parking lot. After realizing we were supposed to show the different ways to represent the pattern within that same pattern we changed it so you will see to the right that we represented the pattern change with the change of colours and the red dots show the change.

Fig.1
Chamberlain, 2015 (C)

I chose to include Figure 2 below because I thought that this group represented the pattern in two very different ways that I would not have thought of when I looked at the pattern. It just goes to show you how very different everybody in a classroom may visualize the same pattern.

Fig. 2
Chamberlain, 2015 (C)

There are some questions I have, not about patterning and algebra, but about teaching math in general. I am always helping with mathematics in my placement because that takes up basically half of their day and I am finding out new things about different learners and coming in situations that I would like some advice on how to address.
For example...
If I am working with students on IEPs with modifications separately, and we are working through questions from the textbook but then they are making mistakes in basic subtraction. Now I have to teach subtraction within teaching another topic. That takes away from the main topic I'm supposed to teach. So what is a good strategy to approach this situation when you have to end up backtracking so far when they do not have these basic skills, without making them more confused than they already are?

How do you include students with needs like these in group collaborative activities when they are so behind?

Also, we learned earlier this semester on different algorithms but in my placement my teacher was going over the lesson topic and when I thought I knew how to solve it he stopped me and showed me the way that the school board wanted it to be taught (different algorithm). But we are learning that students should come up with their own algorithms and that there are many ways to solve problems. So I would like to know about the documents that tell us what and how we are supposed to teach our subjects.

I find that in class there is a lot of focus on the topic of the week and the reading and activities for the topic. But I hope we can include some discussions on difficult situations that will come up in our placement and how to deal with them. Especially when it comes to students on IEPs because the majority of these students have modifications and accommodations in math and I want to be prepared for how I can change my activities and lessons to be more inclusive towards them and in ways that will be clear to them.

Week 6: Report and Reflection

This week we looked at Ratio, Rate and Proportional thinking, in a nutshell the main ideas are:

• Proportional reasoning in the deliberate use of multiplicative relationships to compare quantities and to predict the value of one quantity based of the values of others
• Ratios, rates, and percents, just like fractions and decimals, are comparisons of quantities. A rate compares quantities with different units, for example, distance to time, or price to number of items. A percent always compares a quantity to 100.
• Solving rate, ratio, or percent problems generally involves representing the rate or ratio in a different form 

Here are some ideas our class had on what we know about ratios:

Chamberlain, 2015 (C)

Chamberlain, 2015 (C)

Chamberlain, 2015 (C)

_________________________________________________________________________________

Our Learning Activity presenter Mathieu got our minds by relating some ratios to real life, which seems to be the essential goal for teaching math. An interesting point he made was that ratios are not introduced until grade 6, but they are introduced in informal ways earlier on. He gave the example of how Kindergarten teachers will say there are 2 eyes for every person. So they are using the ratio 2:1.

When we relate math to real life, students have a better understanding of how math shapes their world, and concepts are well remembered when they can be associated with what they already know to be true.

An example of ratios in salad dressing.
A good dressing is typically 2 parts oil and 1 part vinegar, the ratio would be 2:1
(Image URL: http://www.tv411.org/sites/default/files/Math16_0.jpg )

I thought the activity that Mathieu had picked out was really great. Students started to find their own algorithms within the activity. For myself, I found the points where the lines would hit an intersection on the grid, and from there you can extend and double your lines to basically connect the dots. Some students complained that it was too hard, but when you focus too much on perfecting the drawing it takes away from the actual meaning of the activity, which is to double the proportions. I thought it was unfair that he was put on the spot and justified his choice of imagery. I think that in order to avoid this type of situation in our classrooms where students are complaining about the difficulty, we as teachers would probably have to do some modelling and do an example together as a class before they did it on their own. Or like some people said to start off with a simple square and then change the shape to something more abstract. I didn't really see the shape difficulty being a factor, I thought it was a really fun way to tie a holiday like halloween into math. But again this shows that as teachers we can never expect what may come up.

Chamberlain, 2015 (C)

I liked how afterwards we talked about how we could extend this activity, or how we could present it with different ways. Mathieu's hand-out also suggested two different ways he would present the activity, for grade 4s: to enlarge the pictures so it is twice as high and twice as wide, and for grade 6s: ask questions such as, "What is the ratio of the pumpkin's eyes." I thought that this was a great addition to the activity because now we are able to start thinking about reusing activities for different grades and meeting different expectations just by asking our students different types of questions.

Don't you hate when someone has changed the aspect ratio on your TV?
(Image URL: http://imgs.xkcd.com/comics/aspect_ratio.png )

Week 5: Report and Reflection

Good job goes out to my fellow Learning Activity presenters Kevon and Zach, another assignment done! So good on us.

This week focused on integers and the majority of class today was spent on our learning activity presentations. I am glad that our text books provide us with very many activities that we can implement into our classrooms, and it is so interesting to see the ways that they are presented by our peers. 

This week since I was a presenter I want to reflect on the lesson I provided:

I put a lot of thought into what I was going to say and introduce my lesson and how it would flow into the activity. I decided I wanted to split my lesson into 3 categories: Minds On (introduction to material), Activity (let's test out what we just learned), and Consolidation (how what we just learned applies to the curriculum expectations and our overall learning). 

2 Rules For Adding and Subtracting
Integers & Cheat Sheet

When it came to presenting I decided I wanted to introduce what integers we were dealing with (positive/negative whole numbers). And ask students what they knew about describing a positive whole number, and use that to relate to what a negative whole number is. I wanted to use that as a lead way into what we were going to look at for the lesson which then lead into the rules, and examples. 

What I was hoping from my plan was that students who were not certain could have some understanding of the integers we were dealing with, and also had a cheat sheet on the board in writing and also a diagram that they could refer back to for the equations we were about to solve. 

I decided to make a larger than life number line using a relatable material, a deck of cards, which were going to be using in our Core Activity as well. I was skeptical on how this would turn out because I was not sure if the students holding the cards had the opportunity to see what was going on. But I also wanted it to be an experience so I thought it was necessary to have volunteers come up to hold the cards. I tried to differentiate for each types of learners; experiential learning, visual learning, written information on cheat sheets, and also oral information. I am hoping that it was effective but I am worried that I could have organized my number line better and remembered to walk through by taking steps to the next answer. Next time I want to make sure that there is enough space, and also that everyone can see the line and the cheat sheet well from where ever they are sitting. In a grade 7 classroom, students could change places with those sitting so that they all have the opportunity to stand up and hold a card and then sit back down and observe.

Larger than Life Deck of Cards Number Line

I chose the card game activity from Making Math Meaningful called Integro, where you basically use your mental math abilities to shout out the sum of all the numbers of the cards everyone in the group has drawn. This was harder in larger groups and I think in the classroom with grade 7 students I would use smaller groups (maybe even groups of 2 for those not as strong in mental math). I would also not use this as an introduction activity, but maybe after a few days of covering examples just to make sure the students have some more experience with the material before putting them on the spot in front of their peers where they could possibly be embarrassed if some know the material and others are not sure. Nicole came up with some suggestions after the activity that it would be a good idea to group those who are stronger together and those who are not as strong together; this could help so that they are not frustrated that others are quicker than them and can give them a more fair chance in playing.

Integro: Find the sum of the numbers (+2)+(+4)+(-5)+(-7) = -6

Overall I am happy with how it went, I felt that there are a few things to be aware of when using this lesson in a grade 7 classroom and practicing it first on my peers allowed for some insight on that. I find that it is hard to be in front of the class and constantly wondering if what you are doing and saying is making an effective impact, because we can't be the observers of our own teaching. I am also aware that not everything is going to go as perfectly as it will in your own head, but it is good that our peers can give us feedback. 

 _________________________________________

A few people asked about the large scale cards I made, here is the How To For Your Own DIY Large Scale Deck of Cards:

Where: Brock's IRC

Materials (all from IRC):

• 6 pieces of large white construction paper 
• about 3 (maybe more) pieces each of black and red construction paper
• 4" Block Ellison Dies (Numbers, Letters, Shamrock, and Heart)
• Tape or Glue
• Laminator (has a cutter on it but bring scissors to cut yourself incase)
• Paper cutter
• Ruler

How:

1. Divide/cut your red/black construction paper into 4" strips (should get about 4 strips per piece).
2. Use Ellison Dies to cut out your shapes - you can put 2-4 pieces in for one cut to save time, but press down a few times to make sure it's made the cut out.
3. Once you have all your numbers/shapes organize them on your pieces of white construction paper. Find where your middle point is and mark it, and you can lay out and tape or glue the outline for two cards on one large sheet of white paper. (I laid out my numbers 1" from the edge and then taped my symbols in relationship to that).
4. When you have laid out and taped down all your numbers and letters you can laminate all your pieces. 
5. Once everything is laminated, use paper cutter to slice excess lamination off, and now cut your white paper at the middle mark so your one large white piece is now two separate cards.

Week 4: Report and Reflection

Week 4's class consisted of the basic understanding of fractions and ways we can implement activities and strategies into teaching fractions.

First things first, a couple of things I learned about how to describe fractions:

• Fractions describe relationships between a part (the numerator) and a whole (the denominator)
• Although there are two numbers we have to think of them as one idea, and the relationship between the two numbers 
• Fractions can be used to represent parts of a region, parts of measurement, parts of a set or group, and division and ratios 
• Fractions have different meanings and we should be able to put these meanings together to compare their equivalency

Dylan began the class with his learning activity presentation, which I think set the bar high for the rest of us. He was confident and well spoken in his presentation and also provided interesting activities, and provided us with a very visually appealing handout with some colourful examples on it, which helped with engagement. An activity of his I especially liked was the grid he provided in his hand out for us to use the pattern blocks on. This allows us to visually compare the shapes to uncover the fractions. 

Comparing Equivalent Fractions: Yellow is 1 Whole : Red in Halves : Blue in Thirds

Anjali had great insight on how we can use patterns when we add and subtract fractions with different denominators. Something I was so nervous and unconfident about I now feel like I am slowly getting a grasp of. So thank you for that Anjali!

Mariska provided the class with an activity for teaching decimals and how we could relate that to fractions. She related her activity back into the strands of the curriculum for grades 4 and 5, which was a great reminder to us that we should not only be collecting these activities, but comparing them to the curriculum and what age groups they are appropriate for as well. Her activity was a useful one for those seeking to teach cross curricular, by adding some visual arts into the lesson! (I know Tim is reading this and thinking typical arts major...) Anyways... This is my weird looking heart that I made:

It is 32/100 squares or 32 hundredths.... or 16/50 .... or 8/25 ..... which divided equals 0.32..... Wow math is cool.

In conclusion, activities with manipulatives are great for teaching fractions since we use fractions to relate to real world situations, such as who ate more pizza than who, and helps us to make sense of it. 

Something I want to think about more is how the teacher differs from a mathematician, how teachers deconstruct and unpack the big ideas of the problems, lend an experience to them, and then reconstruct them. 

http://cliparts.co/pizza-pictures-cartoon

Week 3: Report and Reflection

What I was primarily fascinated with this week was the way our brain learns and interprets math. In the video below Brain Crossing, Jo Boaler explains what brain crossing is, she says that pathways of our brain light up when we think about symbols and numbers and other pathways light up when we visualize, draw, or estimate with numbers. And when both of these pathways cross, when we think of numbers and start visualizing and drawing them, that is the most powerful math learning.

https://www.youtube.com/watch?v=qZBjub36Bvs

In class Friday we preformed two activities that got us using visualizing and drawing with numbers. The first activity the class divided in half and on separate boards created addition and subtraction problems we thought to be difficult and then had to rank the other groups questions from hardest to easiest. Between the two groups rankings, there was a commonality that fractions seemed to be ranked the hardest because of different denominators. Personally, on the spot I can not remember how to solve fractions at all, having not taken math in about 6-7 years. So for me to find this the hardest was stemmed from not understanding the underlying principles to find an algorithm that could be written on the board.

Board reads: "Too much extra work to make them all the same" and "the common denominator is extremely hard to find."

Our second activity was with base-ten blocks and using these manipulatives to show the different outcomes of ways we can find answers. For example, we were asked to represent with the blocks 56-23. They way I would approach this was to have my 5 longs and 6 units and take away 2 longs and 3 units to come up with my answer. Mathieu presented a different method to the class where he took another set of 2 longs and 3 units and compared it to his 5 longs and 6 units and took away from that to get his answer. His method was more of a visual comparison, where mine was more of an approach of applying the logic that we new each long represented 10 units. In the end, we both came up with the same answer, just in different ways.

These examples in class all relate back to the main ideas represented in this weeks reading. That there are many procedures, or algorithms, for adding, subtracting, multiplying, dividing, etc. The traditional methods we use is just one algorithm and not necessarily better than the others. It is valuable for students to participate in learning activities like the ones above so that they have the opportunities to invent their own procedures and to see the procedures others come up with. It was valuable to the class when Mathieu presented his different approach with the base-ten blocks.

As teachers we should be aware of the alternative and multiple algorithms our students may come up with. We should not worry about how to present these algorithms or how many to present to our students, as long as procedures are taught with meaning to the principles of operation, students can invent their own algorithms themselves. We should let students continue the use of their invented algorithms, and encourage them to record in whatever way is meaningful to them as long as it is understandable by someone who is reading it. Our role is to provide students with the understanding to the underlying principles of the problems and with the appropriate language used in mathematics so that they are able to think more holistically about numbers and how they work.

Week 2: Report and Reflection

I believe there is a stigma with mathematics. When the subject of math comes up most people connect that with negative experiences. I know I do that myself, and the majority of our class announced in their introductions that they were not the best with the subject or have not done it in a while, and there seemed to be some nervousness in that. Also in our social culture math seems to be viewed with the same hesitancy for the subject, in the video Hollywood Hates Math we are presented with streams of clips from different movies where math is something that adds to their character development. Math either takes a back seat, or characters present that they're not good at math, or they are the "freaky math girl," these all add to a negative stereotype of how our culture views math.

https://youtu.be/3uYBoWH3nFk

Regardless of these issues, as teachers our job is to find ways to make mathematics accessible to learn for all students and in a way that will serve them throughout their lives. Teachers and students, as well as parents, all play a part in the curriculum responsibilities so that students will meet the expectations, and more importantly understand the material. Students must bring a willingness to learn and teachers and parents should be their for guidance and encouragement through their process. Parents as well should be discussing the work with their child at home and becoming aware of the curriculum and expectations. They should communicate with their child about their progress and stimulate their interest in mathematics.

As teachers, we must develop appropriate instructional strategies that will help students achieve and develop appropriate methods for evaluation so that students are provided with numerous opportunities to be able to solve problems, reason mathematically, and relate their knowledge and skills to the world around them. We must teach our students to understand, not memorize and regurgitate things that do not make sense for them. Teach them that the answer is only a product and the solution is evaluating the whole thinking process itself. But also understanding ourselves that people can learn better when they are able to connect, and using human experience as a way for students to relate their knowledge and understanding to what makes sense in their world.

The curriculum outlines overall expectations and specific expectations, our five strands of content expectations (or our "big ideas") and our process expectations (problem solving, reasoning and proving, reflecting, selecting tool and computational strategies, connecting, representing, and communicating).

But as a teacher it is important to be able to use different instructional techniques in order to relay these expectations into the class room. Group activities are helpful and game techniques can be used in the classroom, students together are like investigators while teachers provide prompts and facilitate learning so that the students may draw conclusions on their own. For example the Handshake game on Friday's class, allowed us to get up and have social interaction by introducing each other (relative to real world experience) along with the "Think, Pair, Share" strategy allowed us to think on our own, share pair up with a partner to see if we had similar views and come up with conclusions to share with our group. Professor Mgombelo also facilitated our learning during our discussions with prompts so that we were able to collectively find the answer. I found this technique extremely effective for a student like me, who needs extra minds around when learning math and interactiveness, since I find it more complicated on my own. The picture below I found was a good basis for math literacy, to understand math we must know that it is grounded in problem solving, find the most efficient way to understand that problem, understand how we come to an answer, and relate it to personal experiences so that it becomes meaningful.

http://www.emsisd.com/Page/27599

Resources:

1. Ministry of Education, The Ontario Curriculum Grades 1-8: Mathematics, 2005. https://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
2. Dr. Joyce Mgombelo. J/I Math Lecture 2 [In class lecture]. 2015 September 19.

Introduction: Welcome!

Welcome to my blog for EBDE 8P29 - Teaching Math! My name is Julia Chamberlain and in this blog I will be reflecting weekly on the pedagogy of math, ideas for learning, and integrating the classroom discussion into a basis for understanding how we teach and how we learn.

I think that there is a stigma when it comes to learning mathematics, that we ourselves can over complicate it and maybe cannot experience learning it to its full potential. I want to use group dynamics for problem solving, through games, activities, and discussions, we can find solutions together and create problem solving techniques.

In this course I am already beginning to learn that it does not matter of your background or experiences in mathematics because we all have the ability to learn it, we just all learn in different ways at different paces. I hope to gain from this course the knowledge to teach the subject, class room techniques, and also create a large scope of activities that can be used in the classroom to better the teaching of mathematics. As we learned in class today, there is a difference between not knowing the solution and just not having found it yet!

Me!